Today, multilevel analytics on educational governance, management, and leadership are common in educational leadership research, drawing on a variety of approaches and academic disciplines. This article develops a threefold critique of the state of the art. First, this article argues that research on higher education leadership often represents an unreflected position regarding the societal role of higher education--decontextualising leadership from external practices and disregarding its internal object. Second, the approaches applied in leadership as a multilevel phenomenon can be problematic. On one end of the spectrum, we find particularist approaches focusing on individual levels representing disparate and often incompatible theoretical perspectives. As these positions rarely communicate, they have difficulties producing a coherent representation of higher education leadership. Universalist approaches, in turn, study leadership on several levels but offer identical conceptual tools for any societal practice, thereby losing the sensibility of the societal, cultural, and economic tasks of higher-education institutions, and for their specific character as institutions for research and teaching. Thirdly, research on educational leadership mostly fail to provide adequate theory of pedagogical interaction and influence. This is a twofold challenge. On the one hand, research lacks a theory of the object of educational leadership, namely teaching and studying. On the other, although research often defines leadership as a process of influence aimed at supporting learning, it lacks a theory able to explain what constitutes this influence. This article elaborates the possibilities for "non-affirmative theory of education" to provide a theory and language to overcome these challenges.